Actuator control apparatus and magnetic disk unit

ABSTRACT

An actuator control system and a magnetic disk device having a hybrid control system. The actuator control system includes an LPF that can be processed by the hardware architecture of a HDD that does not include a state estimator. The actuator control system includes an actuator  10,  a VCM driver circuit  11  for driving the actuator  10,  an ADC  12  for converting the position signal from the actuator  10  into a digital position signal, an MPU  13  for generating the control signal to the actuator  10  in response to the digital position signal, a DAC  14  for converting the control signal into an analog control signal, and an LPF  15  coupled between DAC  14  and VCM driver circuit  11.  The MPU  13  compensates the phase delay resulting from the LPF  15  by digital control. Additionally, the digital control reconstructs the state model of a plant including the LPF  15  to a state model requiring no state estimator.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is related to an actuator control system of amagnetic storage device, and specifically to an actuator control systemthat reduces the effects of aliasing inherent in the digital control.

2. Description of Related Art

The performance of an actuator control of a magnetic storage device,such as a hard disk drive (HDD), may be degraded by the aliasing causedby the mechanical resonances of a head suspension. In particular, themechanical resonances resulting from the head gimbal assembly (HGA) andthe actuator may reduce the robustness of a HDD, and furthermore raisethe acoustic noise during a high-speed seek operation of a HDD.

One conventional approach to address the effects of such mechanicalresonances is presented in the Japan Published Unexamined PatentApplication No. 5-166312. According to this publication, a low passfilter (LPF) having a low pole is placed immediately after adigital-to-analog converter (DAC) to reduce the gain in the highfrequency region where the resonance is located. Because the LPF alsoaffects characteristics in the low frequency region, the effect of theLPF in the low frequency region is digitally compensated. This actuatorcontrol system is often referred to as a hybrid system because itincorporates a combination of analog and digital circuits.

Although the hybrid actuator control system described above has manydesirable characteristics, it was designed based on the presumption thatthe HDD includes hardware with a processor having relatively higharithmetic processing power.

More specifically, this conventional approach was designed to operatewith a state estimator to meet the high arithmetic processing power ofthe DSP. Unfortunately, such a high performance processor oftenincreases the overall cost of a HDD. As a result, many currentlyavailable HDDs do not include such a processor; therefore, thisconventional hybrid actuator control system approach may not be suitablefor many HDDs available today. Accordingly, it is often desirable tosimplify the algorithm to the extent that it can be processed by anordinary microprocessor (MPU) (i.e., a processor without a stateestimator) while taking advantage of the desirable characteristics ofthe hybrid control system.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an actuator controlsystem and a magnetic disk device that includes a the hybrid controlsystem with a low pass filter (LPF).

It is also an object of the present invention to provide a hybridactuator control system having a LPF that can be processed without astate estimator.

The present invention describes an actuator control system that respondsto the position signal from an actuator. The actuator is driven by acontrol signal which is generated by a driver circuit. The actuatorcontrol system includes a LPF coupled between a digital-to-analogconverter (DAC) for converting the digital control signal into an analogcontrol signal and the driver circuit. Furthermore, the actuator controlsystem includes a digital control device for compensating the phasedelay caused by the LPF by digital control. The digital control devicereconstructs the state model of a plant including the LPF to a statemodel using only directly observable state variables. This may beaccomplished without requiring a state estimator. Furthermore, thedigital control device collectively compensates for the phase delay dueto the LPF as part of the plant when designing the feedback system.

The present invention also describes an actuator control system thatresponds to the position signal from an actuator. The actuator is drivenby a control signal which is generated by a driver circuit. The actuatorcontrol system includes a LPF coupled between a DAC for converting thedigital control signal into an analog control signal and the drivercircuit. The actuator control system also includes a digital controldevice for compensating the phase delay caused by the LPF by digitalcontrol. The digital control device is designed to operate with a stateequation of a system having a LPF converted into a controllablecanonical form as shown by Equations (9) and (10). This conversionenables all state variables to be directly measured. $\begin{matrix}{\begin{bmatrix}{x(i)} \\{v(i)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w(i)}\end{bmatrix} = {\begin{bmatrix}{1 - a_{3}} & {1 + {2a_{3}}} & a_{3} & p_{2} & p_{3} & p_{4} & 0 \\{- a_{3}} & {1 + {2a_{3}}} & a_{3} & p_{2} & p_{3} & p_{4} & 0 \\1 & {- 1} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix} \times {{\begin{bmatrix}{x\left( {i - 1} \right)} \\{v\left( {i - 1} \right)} \\{x\left( {i - 3} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{u\left( {i - 4} \right)} \\{w\left( {i - 1} \right)}\end{bmatrix} + {\begin{bmatrix}p_{1} \\p_{1} \\0 \\1 \\0 \\0 \\0\end{bmatrix}\quad {u\left( {i - 1} \right)}}}}}} & {{Equation}\quad (9)} \\{{y(i)} = {\left\lbrack {1\quad 0\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack \quad\begin{bmatrix}{x(i)} \\{v(i)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w(i)}\end{bmatrix}}} & {\text{Equation}\quad (10)}\end{matrix}$

where

x(I): control output

x(I-1), x(I-2), x(I-3): previous values of x(I)

u(I): control input

u(I-1), u(I-2), u(I-3): previous values of u(I)

v(I): state variable of quasi speed term

w(I): integral term of output

y(I): output of ADC.

One aspect of the present invention includes a digital control devicethat is adapted to control a system having a LPF based on the statefeedback shown by Equation (11). $\begin{matrix}{{u(i)} = {\left\lbrack {f_{1}\quad f_{2\quad}\quad f_{3}\quad f_{4}\quad f_{5}\quad f_{6}\quad f_{7}} \right\rbrack \quad\begin{bmatrix}{x(i)} \\{v(i)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w(i)}\end{bmatrix}}} & {\text{Equation}\quad (11)}\end{matrix}$

where f₁, f₂, f₃, f₄, f₅, f₆, f₇: parameters, and

x(I): control output

x(I-2): previous value of x(I)

u(I): control input

u(I-1), u(I-2), u(I-3): previous values of u(I)

v(I): state variable of quasi speed term

w(I): integral term of output.

Another aspect of the present invention includes a digital controldevice designed with the state equation of a system having a LPF bybeing converted into a controllable canonical form of a speed systemshown by Equations (12) and (13). $\begin{matrix}{\begin{bmatrix}{v(i)} \\{v\left( {i - 1} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w_{v}(i)}\end{bmatrix} = {\begin{bmatrix}{1 + a_{3}} & {- a_{3}} & p_{2} & p_{3} & p_{4} & 0 \\1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 1\end{bmatrix} \times {{\begin{bmatrix}{v\left( {i - 1} \right)} \\{v\left( {i - 2} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{u\left( {i - 4} \right)} \\{w_{v}\left( {i - 1} \right)}\end{bmatrix} + {\begin{bmatrix}p_{1} \\0 \\1 \\0 \\0 \\0\end{bmatrix}\quad {u\left( {i - 1} \right)}}}}}} & {{Equation}\quad (12)} \\{{y_{v}(i)} = {\left\lbrack {1\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack \quad\begin{bmatrix}{v(i)} \\{v\left( {i - 1} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w_{v}(i)}\end{bmatrix}}} & {\text{Equation}\quad (13)}\end{matrix}$

where

v(I): control speed

u(I): control input

u(I-1), u(I-2), u(I-3): previous values of u(I)

y_(v)(I): quasi speed

w_(v)(I): integral of y_(v)(I)

An additional aspect of the present invention includes a digital controldevice that provides a transfer function matrix G from the stateequation of a system including the low pass filter by a calculationbased on Equation (4). $\begin{matrix}\begin{matrix}{G = {{C\left( {{zI} - A} \right)}^{- 1}B}} \\{= \frac{{p_{1}z^{- 1}} + {p_{2}z^{- 2}} + {p_{3}z^{- 3}} + {p_{4}z^{- 4}}}{1 - {\left( {2 + a_{3}} \right)z^{- 1}} + {\left( {1 + {2a_{3}}} \right)z^{- 2}} - {a_{3}z^{- 3}}}}\end{matrix} & {{Equation}\quad (4)}\end{matrix}$

where p₁, p₂, p₃, and p₄ respectively are:

p₁=b₁₁

p₂=a₁b₃₁+b₁₂+b₂₁−a₃b₁₁−b₁₁

p₃=ab₁₁−b₁₂−ap₃b₁₂−a₃b₂₁+b₂₂−a₁b₃₁+a₂b₃₁+a₁b₃₂

p₄=a₃b₁₂−a₃b₃₂+a₂b₃₂

where

G: transfer function matrix

I: unit matrix

A, B: constants.

The transfer function of Equation (4) is reconstructed to a discretestate equation based on the input u, output y, and delay values of themto obtain the controllable canonical form shown by Equations (5) and(6). A control system is designed based on the controllable canonicalform represented by expressions (5) and (6). $\begin{matrix}{\begin{bmatrix}{x(i)} \\{x\left( {i - 1} \right)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)}\end{bmatrix} = {\begin{bmatrix}{2 + a_{3}} & {- \left( {1 + {2a_{3}}} \right)} & a_{3} & p_{2} & p_{3} & p_{4} \\1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0\end{bmatrix} \times {{\begin{bmatrix}{x\left( {i - 1} \right)} \\{x\left( {i - 2} \right)} \\{x\left( {i - 3} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{u\left( {i - 4} \right)}\end{bmatrix} + {\begin{bmatrix}p_{1} \\0 \\0 \\1 \\0 \\0\end{bmatrix}\quad {u\left( {i - 1} \right)}}}}}} & {{Equation}\quad (5)} \\{{y(i)} = {\left\lbrack {1\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack \quad\begin{bmatrix}{x(i)} \\{x\left( {i - 1} \right)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)}\end{bmatrix}}} & {\text{Equation}\quad (6)}\end{matrix}$

where

x(I): control output

x(I-1), x(I-2), x(I-3): previous values of x(I)

u(I): control input

u(I-1), u(I-2), u(I-3), u(I-4): previous values of u(I)

A further aspect of the present invention includes a digital controldevice that provides an output differential which is referred to as aquasi speed term. This term is introduced into a controllable canonicalform as state variable v(I). The control system is designed based on thecontrollable canonical form into which the state variable v(I) isintroduced according to Equation (7).

v(I)=x(I)−x(I-1)  Equation (7)

where x(I) is a control output, and x(I-1) is a previous value of it

The above digital control device may be the one in which the integralterm of the output is further introduced into the controllable canonicalform as a state variable w(I). The control system is designed based onthe controllable canonical form into which the state variable w(I)according to Equation (8).

w(I)=w(I-1)+x(I-1)  Equation (8)

where w(I-1) is a previous value of the state variable w(I) and x(I-1)is a previous value of the control output x(I).

Other objects, features, and advantages of the present invention will beapparent from the accompanying drawings and from the detaileddescription below.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example and notlimitation in the figures of the accompanying drawings, in which likereferences indicate similar elements, and in which:

FIG. 1 illustrates a block diagram of an actuator control system for amagnetic storage system according to one embodiment of the presentinvention;

FIG. 2 is a graph showing the frequency characteristics in the casewhere a low-pass filter (LPF) with a cutoff frequency f_(c) is inserted;and

FIG. 3 is a graph showing the frequency characteristics in which losscaused by the insertion of the LPF in the low frequency region has beendigitally compensated for.

DETAILED DESCRIPTION

The actuator control system of the present invention may be used withthe head position control system of a hard disk drive (HDD) or the like.

FIG. 1 illustrates an actuator control system according to oneembodiment of the present invention. In FIG. 1, the actuator controlsystem includes an actuator 10 with a head suspension mechanism 17 and ad.c. motor for moving the head (e.g. a voice coil motor (VCM) 16). A VCMdriver circuit 11 drives VCM 16 of actuator 10. The head suspensionmechanism 17 rotates around a pivot (not shown). An analog-to-digitalconverter (ADC) 12 converts a position signal y (t) provided by actuator10 to a digital position signal. The position signal y(t) represents theposition of head 18. A microprocessor (MPU) 13, which is responsive tothe digital position signal, generates a control signal for moving thehead to a desired position based on a state feedback shown by Equation11 to be described later. For alternative embodiments, it is notrequired that the digital control device is implemented with amircroprocessor. A digital-to-analog converter (DAC) 14 converts thedigital control signal from MPU 13 to an analog control signal u(t). Ananalog low pass filter (LPF) 15 is coupled between DAC 14 and VCM drivercircuit 11.

The LPF 15 which is positioned between DAC 14 and VCM driver circuit 11is a first order analog LPF with a low pole. The analog LPF 15 reducesthe gain of the high-frequency band in which mechanical resonanceexists. For alternative embodiments, LPF 15 may be a digital LPF. Thefrequency characteristics of LPF 15 are described later in accordancewith FIG. 2.

The MPU 13 generates a control signal for moving the head to a desiredposition in accordance with Equation (11) described later. The controlsystem represented by Equation (11) compensates, by digital control, forthe phase delay in a band ower than the Nyquist frequency fN, resultingfrom the analog LPF 15. The control system of the present invention is asimplified control system for providing digital control withoutrequiring a state estimator. Thus, the actuator control system of thepresent invention may be processed by the hardware architecture in manyHDDs available today.

The operation of the actuator control system is described below. Theanalog LPF 15 causes a phase delay in a band lower than the Nyquistfrequency fN. The actuator control system of the present inventioncompensates this phase delay by digital control.

FIG. 2 shows the frequency characteristics of an actuator control systembefore the phase delay in a band lower than the Nyquist frequency fN iscompensated by digital control. FIG. 3 shows the frequencycharacteristics of the actuator control system after such phase delayhas been compensated. In these figures, the ordinate represents the gainand the abscissa represents the frequency.

The dotted line in FIG. 2 represents the frequency characteristics of acontrolled system that includes actuator 10. Furthermore, a peak in thefrequency characteristics due to mechanical resonance occurs in ahigh-frequency region above the Nyquist frequency fN.

The LPF 15 provides an attenuation characteristic in which apredetermined amount of attenuation occurs in a frequency region higherthan the cutoff frequency fc, as shown by the solid line in FIG. 2. Thiscauses the peak of the frequency characteristics caused by mechanicalresonance, which occurs in a high-frequency region above the Nyquistfrequency fN, to be attenuated.

Additionally, the LPF 15 enables the loss (phase delay) occurring in alow-frequency region (i.e., the region between the cutoff frequency fcand the Nyquist frequency fN) to be compensated by digital control. Thehatched region shown in FIG. 2 illustrates the attenuated portion in thelow-frequency region. Thus, the region between the cut-off frequency fcand the Nyquist frequency fN displays characteristics similar to that ofa control system that does not include a LPF. As a result of digitallycontrolling the region lower than the Nyquist frequency fN, thefrequency characteristics of the region lower than the Nyquist frequencyfN can be digitally compensated. Thus, only the high-frequency region,which includes the peak of the frequency characteristics caused bymechanical resonances, is largely attenuated. FIG. 3 shows the frequencycharacteristics after the compensation by digital control. The hatchedportion in FIG. 3 represents the attenuated portion.

The present invention describes a design technique used to compensatethe phase delay in the region lower than the Nyquist frequency fNresulting from the LPF 15. The design technique of the present inventionimplements digital control with a simplified control system which can beprocessed without a state estimator. As mentioned above, many HDDscurrently available today do not have a state estimator.

As mentioned above, actuator 10 of the HDD includes the current drivenVCM 16 and arm 17 which supports the movement of magnetic head 18. Thedrive current of VCM 16 is usually proportional to the output valueprovided by MPU 13 through DAC 14. Accordingly, the control inputreceived by actuator 10 represents acceleration information and thecontrol output provided by actuator 10 represents position information.The basic system is referred to as a quadratic integral system.

If the first order LPF 15 is placed on the output side of DAC 14, thetransfer function g(s) of the object to be controlled, including thefirst order LPF 15, becomes a three order system as shown by Equation(1). $\begin{matrix}{{g(s)} = {{{y(s)}\text{/}{u(s)}} = \frac{b}{s^{2}\left( {s + a} \right)}}} & {{Equation}\quad (1)}\end{matrix}$

In Equation (1), u is the output of DAC 14, which represents the controlinput. Further, y is a position error signal (PES), which represents thecontrol output. Note that “a” represents the pole of LPF 15, “b”represents the d.c. gain of the system, and “s” represents a Laplaceoperator.

Equations (2) and (3) represent a discrete version of Equation (1)having a sampling interval T and a calculation time delay

x(I+1)=Ax(I)+Bu(I)  Equation (2)

y(I)=Cx(I)  Equation (3)

where ${x(i)} = \begin{bmatrix}{x(i)} \\{{{dx}(i)}/{dt}} \\{d^{2}{{x(i)}/{dt}^{2}}}\end{bmatrix}$ ${u(i)} = \begin{bmatrix}{u(i)} \\{u\left( {i - 1} \right)}\end{bmatrix}$ $A = \begin{bmatrix}1 & T & a_{1} \\0 & 1 & a_{2} \\0 & 0 & a_{3}\end{bmatrix}$ $B = \begin{bmatrix}b_{11} & b_{21} \\b_{21} & b_{22} \\b_{31} & b_{32}\end{bmatrix}$ C = [1  0  0]

A conventional control system based on Equations (2) and (3) isdescribed in the Japan Publication of Unexamined Patent Application No.5-166312 previously mentioned. In this control system, a gain parameterfor collectively compensating the LPF and the quadric integral system,which is the primary system, is obtained by a publicly known optimumcontrol theory (for instance, the LQ method), such that the naturalfrequency characteristics are obtained for both the closed and openloops.

Of the state variables x(I), dx(I)/dt, and d2x(I)/dt2 which representthe position, speed, and acceleration of the head, respectively, onlyx(I) can be directly observed, and thus the remaining dx(I)/dt andd2x(I)/dt2 are estimated using a state estimator. By using a Kalmanfilter as the state estimator and appropriately using the current typeand the prediction type depending on the case, a stable operation couldbe continued with no effect on the behavior of the whole control systemeven if the PES for one sample was dropped because of some failure.However, since the use of the state estimator is based on thepresumption that a microprocessor or DSP having a high arithmeticprocessing power is used as hardware, the processing speed of themicroprocessor (MPU) of many current HDD is not sufficient.

Accordingly, it is desirable to simplify the algorithm to the extentthat it can be processed by a microprocessor (MPU) having lessprocessing power such as one without a state estimator.

For the present invention, the realization of the system shown by theabove Equations (2) and (3) is designed after converting them to acontrollable canonical form. This realization allows all state variablesto be directly measured. As a result, the state estimator can beeliminated. Furthermore, since the closed loop is designed tocollectively compensate the LPF and the original second order system,natural characteristics are easily obtained. The LQ method can also beapplied to the actuator control system of the present invention.However, since there is no state estimator, the precision of theinterpolation for dropped samples decreases.

The transfer function matrix G of the system shown by the aboveEquations (2) and (3) is determined. Then, if I is a unit matrix of anappropriate dimension, the transfer function matrix G is represented byEquation (4). $\begin{matrix}\begin{matrix}{G = {{C\left( {{zI} - A} \right)}^{- 1}B}} \\{= \frac{{p_{1}z^{- 1}} + {p_{2}z^{- 2}} + {p_{3}z^{- 3}} + {p_{4}z^{- 4}}}{1 - {\left( {2 + a_{3}} \right)z^{- 1}} + {\left( {1 + {2a_{3}}} \right)z^{- 2}} - {a_{3}z^{- 3}}}}\end{matrix} & {{Equation}\quad (4)}\end{matrix}$

where p₁, p₂, p₃, and p₄ respectively are:

p₁=b₁₁

p₂=a₁b₃₁+b₁₂+b₂₁a₃ ₁₁−b₁₁

p₃=a₃b₁₁−b₁₂−a₃b₁₂−a₃b₂₁+b₂₂−a₁b₃₁+a₂b₃₁+a₁b₃₂

p₄=a₃b₁₂−a₃b₂₂−a₁b₃₂+a₂b₃₂

Equations (5) and (6) represent the transfer function of Equation (4)converted into discrete state equations based on the input u, output y,and their respective delay values. Equations (5) and (6) may be achievedby employing a controllable canonical form. $\begin{matrix}{\begin{bmatrix}{x(i)} \\{x\left( {i - 1} \right)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)}\end{bmatrix} = {\begin{bmatrix}{2 + a_{3}} & {- \left( {1 + {2a_{3}}} \right)} & a_{3} & p_{2} & p_{3} & p_{4} \\1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0\end{bmatrix} \times {{\begin{bmatrix}{x\left( {i - 1} \right)} \\{x\left( {i - 2} \right)} \\{x\left( {i - 3} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{u\left( {i - 4} \right)}\end{bmatrix} + {\begin{bmatrix}p_{1} \\0 \\0 \\1 \\0 \\0\end{bmatrix}\quad {u\left( {i - 1} \right)}}}}}} & {{Equation}\quad (5)} \\{{y(i)} = {\left\lbrack {1\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack \quad\begin{bmatrix}{x(i)} \\{x\left( {i - 1} \right)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)}\end{bmatrix}}} & {\text{Equation}\quad (6)}\end{matrix}$

In the above Equations (5) and (6), x(I) is a control output, x(I-1) isthe previous value immediately before it, and x(I-2) and x(I-3) are thesecond and third previous values of it, respectively. Further, u(I) is acontrol input, u(I-1) is the previous value immediately before it, andu(I-2) and u(I-3) are the second and third previous values of it,respectively.

Note that all factors other than x(I) and u(I) can be represented by theprevious values of both the control output x(I) and control input u(I),or by values which can be directly observed (they may be saved in amemory).

It is often more convenient if the output differential, namely, thequasi speed term v(I), positively appears as a state variable. The quasispeed term v(I) is defined in Equation 7. Furthermore, if the integralterm w(I) of the output is introduced as a state variable according toEquation (8), the system can be expressed by seven orders as shown byEquations (9) and (10). The HDD often has noise due to the effect offlexible tension or wind, and thus the error does not converge to zeroonly with the feedback shown by the Equations (5) and (6). To achievesuch convergence, it is needed to introduce the integral term w(I) forintegrating the error between the actual position and the targetposition, and enable the above error convergence by the integral termw(I).

v(I)=x(I)−x(I-1)  Equation (7)

where x(I) is a control output, and x(I-1) is a previous value of it.

w(I)=w(I-1)+x(I-1)  Equation (8)

where w(I-1) is a previous value of the state variable w(I), and x(I-1)is a previous value of the control output x(I). $\begin{matrix}{\begin{bmatrix}{x(i)} \\{v(i)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w(i)}\end{bmatrix} = {\begin{bmatrix}{1 - a_{3}} & {1 + {2a_{3}}} & a_{3} & p_{2} & p_{3} & p_{4} & 0 \\{- a_{3}} & {1 + {2a_{3}}} & a_{3} & p_{2} & p_{3} & p_{4} & 0 \\1 & {- 1} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix} \times {{\begin{bmatrix}{x\left( {i - 1} \right)} \\{v\left( {i - 1} \right)} \\{x\left( {i - 3} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{u\left( {i - 4} \right)} \\{w\left( {i - 1} \right)}\end{bmatrix} + {\begin{bmatrix}p_{1} \\p_{1} \\0 \\1 \\0 \\0 \\0\end{bmatrix}\quad {u\left( {i - 1} \right)}}}}}} & {{Equation}\quad (9)} \\{{y(i)} = {\left\lbrack {1\quad 0\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack \quad\begin{bmatrix}{x(i)} \\{v(i)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w(i)}\end{bmatrix}}} & {\text{Equation}\quad (10)}\end{matrix}$

The state feedback shown by Equation (11) is constructed from Equations(9) and (10). More specifically, the system represented by Equations (9)and (10) may be used as a model to determine (i.e., by experiment)parameters f1 to f7 of the Equation (11) so as to optimize the feedback.The MPU 13 performs a seven-order calculation based on the Equation (11)to carry out the actuator control including the above described digitalcompensation. $\begin{matrix}{{u(i)} = {\left\lbrack {f_{1}\quad f_{2}\quad f_{3}\quad f_{4}\quad f_{5}\quad f_{6}\quad f_{7}} \right\rbrack \quad\begin{bmatrix}{x(i)} \\{v(i)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w(i)}\end{bmatrix}}} & {{Equation}\quad (11)}\end{matrix}$

The conventional discrete system using no LPF includes an integrator,and may be represented by five orders. Accordingly, the control systemof the present embodiment increases from five orders to seven orders,and thus the increase in the sum of products in the state feedback istwo sets at most.

The system of the Equations (9) and (10) represents a position system,and it is used for the control system design of settling and trackfollowing. On the other hand, a speed system is usually used forcontrolling a seek operation. If the integral term is excluded fromEquations (9) and (10) and x(I) is considered to be the integral ofv(I), an identical setting is also available from Equations (9) and(10). For reference, Equations (12) and (13) represents a speed system.$\begin{matrix}{\begin{bmatrix}{v(i)} \\{v\left( {i - 1} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w_{v}(i)}\end{bmatrix} = {\begin{bmatrix}{1 + a_{3}} & {- a_{3}} & p_{2} & p_{3} & p_{4} & 0 \\1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 1\end{bmatrix} \times {{\begin{bmatrix}{v\left( {i - 1} \right)} \\{v\left( {i - 2} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{u\left( {i - 4} \right)} \\{w_{v}\left( {i - 1} \right)}\end{bmatrix} + {\begin{bmatrix}p_{1} \\0 \\1 \\0 \\0 \\0\end{bmatrix}\quad {u\left( {i - 1} \right)}}}}}} & {{Equation}\quad (12)} \\{{y_{v}(i)} = {\left\lbrack {1\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack \quad\begin{bmatrix}{v(i)} \\{v\left( {i - 1} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w_{v}(i)}\end{bmatrix}}} & {\text{Equation}\quad (13)}\end{matrix}$

where y_(v)(I) and w_(v)(I) are a quasi speed and the integrationthereof, respectively.

As described above, the actuator control apparatus related to thepresent embodiment comprises actuator 10, VCM driver circuit 11 fordriving the actuator 10, ADC 12 for converting the position signal fromthe actuator 10 to a digital position signal, MPU 13 for generating acontrol signal to for actuator 10 in response to the digital positionsignal, DAC 14 for converting the digital control signal to an analogcontrol signal, and LPF 15 coupled between DAC 14 and VCM driver circuit11. The MPU 13 compensates the phase delay resulting from LPF 15 bydigital control. The digital control is implemented by a control systemwhich is constructed so that the state model of a plant including LPF 15is reconstructed to a state model using only directly observable statevariables without requiring a state estimator. Thus, the phase delay dueto the interposition of the LPF 15 is collectively compensated as partof the plant when designing the feedback system.

In the present embodiment, this control system is obtained by (1)designing it after converting the state equation of a system includingLPF 15 into a controllable canonical form and (2) having MPU 13 generatea control signal for moving the head to a desired position according tothe feedback control shown by Equation (11). Thus, the presentembodiment can be expressed by a seven order state feedback as shown byEquation (11), and it can be implemented by a simplified control systemprocessable by the hardware architecture of the many currently availableHDDs without requiring a state estimator. Accordingly, since the digitalcontrol includes the type of microprocessor used in many currentlyavailable HDDs (i.e., without using a DSP), the actuator controlapparatus of the hybrid control system which has excellentcharacteristics, can be implemented at low cost.

For one embodiment, the pole of the analog LPF 15 was placed at 1.6 kHz.The LPF 15 was implemented by changing the capacitor originally put inthe VCM driver circuit 11 to that having a larger value. Accordingly,the addition of LPF 15 to the actuator control system did not requireany increase in cost or substrate area.

An improvement in the gain equal to or larger than 5 dB was observed ina band higher than the Nyquist frequency. As a result, the robustnessfor mechanical resonance was increased. Furthermore, the acoustic noisewas also improved by 4 dB at 8 kHz for instance. Additionally, the seektime was not degraded.

Several advantages of the present invention are described below. Thefollowing advantages can be obtained without sacrificing the accessspeed in a HDD.

(1) The robustness in a band higher than the Nyquist frequency fN can beincreased. That is, the increase of the robustness can be achieved in asimplified control system processable by the hardware architecture ofthe many currently available HDDS. Additionally, the reliability of theproduct increases and the yield in the process can be improved.

(2) The acoustic noise in the seek operation can be reduced.

(3) The damping parts attached to the HDD may be eliminated in order toreduce the cost.

Accordingly, if the actuator control apparatus having such excellentadvantages is applied to the position control system of a HDD, thenthere is no reduction in the robustness of the HDD due to the respectivemechanical resonance of the head gimbal assembly (HGA) and the actuator,and no acoustic noise resulting from the high-speed seek operation.Thus, since the microprocessor does not require a DSP, the actuatorcontrol system of the present invention may be implemented in manycurrently available HDDs without increasing the hardware costs.

Although the present embodiment, has been described with respect to ahead position control system of a HDD, the hybrid control system of thepresent invention may be used in various other applications. Forexample, the apparatus may be used for the position control of anexternal storage device other than the HDD or any other control system.That is, the object to be controlled is not limited as long as it is acontrol system including the state feedback shown by the Equations (9),(10), and (11).

Furthermore, in addition to the method described in the presentembodiment, there are other methods for achieving the actuator controlapparatus related to the present embodiment without using a stateestimator, as long as they are the ones in which the state model of aplant including a LPF is reconstructed to a state model requiring nostate estimator.

While the preferred embodiments of the present invention have beenillustrated in detail, it should be apparent that modifications andadaptations to those embodiments may occur to one skilled in the artwithout departing from the scope of the present invention as set forthin the following claims.

What is claimed is:
 1. An actuator control apparatus for providing acontrol signal to an actuator driven by a driver circuit in response toa position signal from said actuator wherein said position signal isused to position a head coupled to said actuator, said actuator controlapparatus comprising: an analog-to-digital converter (ADC) forconverting said position signal into a digital position signal; adigital control device coupled to said ADC, said digital control devicereceiving said digital position signal and providing a digital controlsignal; a digital-to-analog converter (DAC) coupled to said digitalcontrol device, said DAC converting said digital control signal into ananalog control signal; and a low pass filter (LPF) coupled between saiddriver circuit and said DAC and receiving said analog control signal,wherein said digital control device reconstructs the state model of aplant which includes said LPF to a state model using only directlyobservable state variables and collectively compensates for the phasedelay resulting from said LPF.
 2. The actuator control apparatus ofclaim 1, wherein said digital control device is based on state Equations(9) and (10), $\begin{matrix}{\begin{bmatrix}{x(i)} \\{v(i)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w(i)}\end{bmatrix} = {\begin{bmatrix}{1 - a_{3}} & {1 + {2a_{3}}} & a_{3} & p_{2} & p_{3} & p_{4} & 0 \\{- a_{3}} & {1 + {2a_{3}}} & a_{3} & p_{2} & p_{3} & p_{4} & 0 \\1 & {- 1} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix} \times {{\begin{bmatrix}{x\left( {i - 1} \right)} \\{v\left( {i - 1} \right)} \\{x\left( {i - 3} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{u\left( {i - 4} \right)} \\{w\left( {i - 1} \right)}\end{bmatrix} + {\begin{bmatrix}p_{1} \\p_{1} \\0 \\1 \\0 \\0 \\0\end{bmatrix}\quad {u\left( {i - 1} \right)}}}}}} & {{Equation}\quad (9)} \\{{y(i)} = {\left\lbrack {1\quad 0\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack \quad\begin{bmatrix}{x(i)} \\{v(i)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w(i)}\end{bmatrix}}} & {\text{Equation}\quad (10)}\end{matrix}$

where x(I): control output x(I-1), x(I-2), x(I-3): previous values ofx(I) u(I): control input u(I-1), u(I-2), u(I-3): previous values of u(I)v(I): state variable of quasi speed term w(I): integral term of outputy(I): output of ADC.
 3. The actuator control apparatus of claim 2,wherein said digital control device provides feedback control based onthe state feedback shown by Equation (11), $\quad \begin{matrix}{{u(i)} = {\left\lbrack {f_{1}\quad f_{2}\quad f_{3}\quad f_{4}\quad f_{5}\quad f_{6}\quad f_{7}} \right\rbrack \quad\begin{bmatrix}{x(i)} \\{v(i)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w(i)}\end{bmatrix}}} & {{Equation}\quad (11)}\end{matrix}$

where f₁, f₂, f₃, f₄, f₅, f₆, f₇: parameters x(I): control outputx(I-2): previous value of x(I) u(I): control input u(I-1), u(I-2),u(I-3): previous values of u(I) v(I): state variable of quasi speed termw(I): integral term of output.
 4. The actuator control apparatus ofclaim 1, wherein said digital control device provides a speed systembased on Equations (12) and (13), $\begin{matrix}{\begin{bmatrix}{v(i)} \\{v\left( {i - 1} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w_{v}(i)}\end{bmatrix} = {\begin{bmatrix}{1 + a_{3}} & {- a_{3}} & p_{2} & p_{3} & p_{4} & 0 \\1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 1\end{bmatrix} \times {{\begin{bmatrix}{v\left( {i - 1} \right)} \\{v\left( {i - 2} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{u\left( {i - 4} \right)} \\{w_{v}\left( {i - 1} \right)}\end{bmatrix} + {\begin{bmatrix}p_{1} \\0 \\1 \\0 \\0 \\0\end{bmatrix}\quad {u\left( {i - 1} \right)}}}}}} & {{Equation}\quad (12)} \\{{y_{v}(i)} = {\left\lbrack {1\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack \quad\begin{bmatrix}{v(i)} \\{v\left( {i - 1} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{w_{v}(i)}\end{bmatrix}}} & {\text{Equation}\quad (13)}\end{matrix}$

where v(I): control speed u(I): control input u(I-1), u(I-2), u(I-3):previous values of u(I) y_(v)(I): quasi speed w_(v)(I): integral ofy_(v)(I).
 5. An actuator control apparatus of claim 1, wherein saiddigital control device provides a transfer function matrix G based onEquation (4), $\begin{matrix}\begin{matrix}{G = {{C\left( {{zI} - A} \right)}^{- 1}B}} \\{= \frac{{p_{1}z^{- 1}} + {p_{2}z^{- 2}} + {p_{3}z^{- 3}} + {p_{4}z^{- 4}}}{1 - {\left( {2 + a_{3}} \right)z^{- 1}} + {\left( {1 + {2a_{3}}} \right)z^{- 2}} - {a_{3}z^{- 3}}}}\end{matrix} & {{Equation}\quad (4)}\end{matrix}$

where p₁, p₂, p₃ and p₄ respectively are: p₁=b₁₁p₂=a₁b₃₁+b₁₂+b₂₁−a₃b₁₁−b₁₁p₃=a₃b₁₁−b₁₂−a₃b₁₂−a₃b₂₁+b₂₂−a₁b₃₁+a₂b₃₁+a₁b₃₂p₄=a₃b₁₂−a₃b₂₂−a₁b₃₂+a₂b₃₂ where G: transfer function matrix I: unitmatrix A, B: constants, wherein said digital control device reconstructssaid transfer function of said equation (4) into a discrete stateequation based on the input u, the output y, and their respective delayvalues, wherein said discrete state equation is represented by Equations(5) and (6), $\begin{matrix}{\begin{bmatrix}{x(i)} \\{x\left( {i - 1} \right)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)}\end{bmatrix} = {\begin{bmatrix}{2 + a_{3}} & {- \left( {1 + {2a_{3}}} \right)} & a_{3} & p_{2} & p_{3} & p_{4} \\1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0\end{bmatrix} \times {{\begin{bmatrix}{x\left( {i - 1} \right)} \\{x\left( {i - 2} \right)} \\{x\left( {i - 3} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)} \\{u\left( {i - 4} \right)}\end{bmatrix} + {\begin{bmatrix}p_{1} \\0 \\0 \\1 \\0 \\0\end{bmatrix}\quad {u\left( {i - 1} \right)}}}}}} & {{Equation}\quad (5)} \\{{y(i)} = {\left\lbrack {1\quad 0\quad 0\quad 0\quad 0\quad 0} \right\rbrack \quad\begin{bmatrix}{x(i)} \\{x\left( {i - 1} \right)} \\{x\left( {i - 2} \right)} \\{u\left( {i - 1} \right)} \\{u\left( {i - 2} \right)} \\{u\left( {i - 3} \right)}\end{bmatrix}}} & {\text{Equation}\quad (6)}\end{matrix}$

where x(I): control output x(I-1), x(I-2), x(I-3): previous values ofx(I) u(I): control input u(I-1), u(I-2), u(I-3), u(I-4): previous valuesof u(I).
 6. The actuator control apparatus of claim 1, wherein saiddigital control device provides a quasi speed term v(I) represented byEquation (7), v(I)=x(I)−x(I-1)  Equation (7) where x(I) is a controloutput, and x(I-1) is a previous value of x(I).
 7. The actuator controlapparatus of claim 6, wherein said digital control device provides anintegral term w(I) represented by Equation (8),w(I)=w(I-1)+x(I-1)  Equation (8) where w(I-1) is a previous value of thestate variable w(I), and x(I-1) is a previous value of the controloutput x(I).
 8. The actuator control apparatus as set forth in claim 1,wherein said low pass filter includes a cut-off frequency set so as tofully attenuate the peak in a frequency region higher than the Nyquistfrequency.
 9. The actuator control apparatus as set forth in claim 1,wherein said low pass filter is an analog first order low pass filterwhich has a pole at a frequency lower than the Nyquist frequency. 10.The actuator control apparatus as set forth in claim 1, wherein said lowpass filter is a digital low pass filter.
 11. The actuator controlapparatus of claim 1, wherein said digital control device is amicroprocessor.
 12. A magnetic disk device, comprising: at least onedisk for storing information; at least one head for reading informationfrom or writing information to at least one of said disks; a suspensioncoupled to said head; an actuator coupled to said suspension, saidactuator providing an analog position signal; an actuator control systemincluding: a driver circuit for driving said actuator; ananalog-to-digital converter (ADC) for converting said analog positionsignal from said actuator into a digital position signal; a digitalcontrol device for providing a digital control signal to said actuatorin response to said digital position signal; a digital-to-analogconverter (DAC) for converting said digital control signal into ananalog control signal; and a low pass filter (LPF) coupled between saidDAC and said driver circuit, wherein said digital control devicereconstructs the state model of a plant including said LPF to a statemodel using only directly observable state variables and collectivelycompensates for the phase delay resulting from said LPF as part of saidplant.